Complete the paragraph proof. We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to . If AB > AC, then m∠C > m∠B by the . If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem. But by the definition of congruent, we know the measure of angle B equals the measure of by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.

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AlonsoDehner AlonsoDehner · Answer 1 · 2018-11-22T01:47:37+01:00

Given that ∠B ≅ ∠C.

to prove that the sides AB = AC

This can be done by the method of contradiction.

If possible let AB [tex]\neq[/tex]=AC

Then either AB>AC or AB<AC

Case i: If AB>AC, then by triangle axiom, Angle C > angle B.

But since angle C = angle B, we get AB cannot be greater than AC

Case ii: If AB<AC, then by triangle axiom, Angle C < angle B.

But since angle C = angle B, we get AB cannot be less than AC

Conclusion:

Since AB cannot be greater than AC nor less than AC, we have only one possibility. that is AB =AC

Hence if angle B = angle C it follows that

AB = AC, and AB ≅ AC.

18107267 18107267 · Answer 2 · 2019-02-08T01:03:37+01:00

Answer:

Segment AC, Converse of the triangle parts relationship theorem, Angle C in that order

Step-by-step explanation:

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